Recursive method to obtain the parametric representation of a generic Feynman diagram
Ivan Gonzalez, Ivan Schmidt
Abstract
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar ϕ3 ϕ4 theory, is presented. The representation is obtained starting from an Initial Parameters Matrix (IPM), which relates the scalar products between internal and external momenta, and which appears explicitly when this parametrization is applied to the momentum space representation of the graph. The final product is an algorithm that can be easily programmed, either in a computer programming language (C/C++, Fortran,...) or in a symbolic calculation package (Maple, Mathematica,...).
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